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Abstract

It is possible to obtain useful maps of surface albedo from remotely sensed images by eliminating effects due to topography and the atmosphere, even when the atmospheric state is not known. A simple phenomenological model of earth radiance that depends on six empirically determined parameters is developed given certain simplifying assumptions. The model incorporates path radiance and illumination from sun and sky and their dependencies on surface altitude and orientation. It takes explicit account of surface shape, represented by a digital terrain model, and is therefore especially suited for use in mountainous terrain. A number of ways of determining the model parameters are discussed, including the use of shadows to obtain path radiance and to estimate local albedo and sky irradiance. The emphasis is on extracting as much information from the image as possible, given a digital terrain model of the imaged area and a minimum of site-specific atmospheric data. The albedo image, introduced as a representation of surface reflectance, provides a useful tool to evaluate the simple imaging model. Criteria for the subjective evaluation of albedo images are established and illustrated for Landsat multispectral data of a mountainous region of Switzerland. The method exposes some of the limitations found in computing reflectance information using only the image-forming equation.

References

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Table I

Surface Slope Angle for Which the Direct Solar Contribution to Target Irradiance Equals the Diffuse Sky Contribution; Values are Given at Various Altitudes and Two Azimuthal Angles for the Atmospheric Model of Fig. 14

Alt. (m)

θn when ϕn − ϕ0 = 180° (degrees)

θn when ϕn − θ0 = 90° (degrees)

0

7

47

410

12

59

1000

17

69

2000

23

78

3210

27

83

Table II

Relative Sensitivities (∂ρ/∂X)/(ρ/X) of Computed Albedo to the Path Radiance Model Parameters X = Lp0 and X = Hp at Various Altitudes for MSS Band 4; Other Parameter Values are Those of Fig. 14; Model Sensor Radiance L is in mW cm−2 sr−1

Alt. (m)

X =

(L = 0.34)

(L = 1.41)

(L = 2.48)

Lp0

Hp

Lp0

Hp

Lp0

Hp

0

−33.000

0.000

−0.306

0.000

−0.153

0.000

500

−4.218

−0.771

−0.242

−0.044

−0.125

−0.023

1000

−2.061

−0.754

−0.194

−0.071

−0.102

−0.037

1500

−1.277

−0.700

−0.156

−0.086

−0.083

−0.046

2000

−0.876

−0.641

−0.127

−0.093

−0.068

−0.050

2500

−0.637

−0.582

−0.104

−0.095

−0.056

−0.052

Table III

Relative Sensitivities (∂ρ/∂X)/(ρ/X) of Computed Albedo to the Sky Irradiance X = Es0 and X = Hs and Optical Depth Model Parameters X = τ0 and X = H for Horizontal Sunlit Targets at Various Altitudes for MSS Band 4; Other Parameter Values are Those of Fig. 14

Alt. (m)

X =

Es0

Hs

τ0

H

0

−0.278

0.000

0.526

0.000

500

−0.240

−0.041

0.477

0.060

1000

−0.207

−0.070

0.432

0.108

1500

−0.177

−0.090

0.390

0.146

2000

−0.151

−0.103

0.350

0.175

2500

−0.129

−0.109

0.314

0.196

Table IV

Relative Sensitivities (∂ρ/∂X)/(ρ/X) of Computed Albedo to the Sky Irradiance X = Es0 and X = Hs and Optical Depth Model Parameters X = τ0 and X = H for Horizontal Shadowed Targets at Various Altitudes for MSS Band 4; Other Parameter Values are Those of Fig. 14

Alt. (m)

X =

Es0

Hs

τ0

H

0

−1.000

0.000

0.230

0.000

500

−1.000

−0.170

0.203

0.025

1000

−1.000

−0.340

0.179

0.045

1500

−1.000

−0.509

0.158

0.059

2000

−1.000

−0.679

0.140

0.070

2500

−1.000

−0.849

0.123

0.077

Tables (4)

Table I

Surface Slope Angle for Which the Direct Solar Contribution to Target Irradiance Equals the Diffuse Sky Contribution; Values are Given at Various Altitudes and Two Azimuthal Angles for the Atmospheric Model of Fig. 14

Alt. (m)

θn when ϕn − ϕ0 = 180° (degrees)

θn when ϕn − θ0 = 90° (degrees)

0

7

47

410

12

59

1000

17

69

2000

23

78

3210

27

83

Table II

Relative Sensitivities (∂ρ/∂X)/(ρ/X) of Computed Albedo to the Path Radiance Model Parameters X = Lp0 and X = Hp at Various Altitudes for MSS Band 4; Other Parameter Values are Those of Fig. 14; Model Sensor Radiance L is in mW cm−2 sr−1

Alt. (m)

X =

(L = 0.34)

(L = 1.41)

(L = 2.48)

Lp0

Hp

Lp0

Hp

Lp0

Hp

0

−33.000

0.000

−0.306

0.000

−0.153

0.000

500

−4.218

−0.771

−0.242

−0.044

−0.125

−0.023

1000

−2.061

−0.754

−0.194

−0.071

−0.102

−0.037

1500

−1.277

−0.700

−0.156

−0.086

−0.083

−0.046

2000

−0.876

−0.641

−0.127

−0.093

−0.068

−0.050

2500

−0.637

−0.582

−0.104

−0.095

−0.056

−0.052

Table III

Relative Sensitivities (∂ρ/∂X)/(ρ/X) of Computed Albedo to the Sky Irradiance X = Es0 and X = Hs and Optical Depth Model Parameters X = τ0 and X = H for Horizontal Sunlit Targets at Various Altitudes for MSS Band 4; Other Parameter Values are Those of Fig. 14

Alt. (m)

X =

Es0

Hs

τ0

H

0

−0.278

0.000

0.526

0.000

500

−0.240

−0.041

0.477

0.060

1000

−0.207

−0.070

0.432

0.108

1500

−0.177

−0.090

0.390

0.146

2000

−0.151

−0.103

0.350

0.175

2500

−0.129

−0.109

0.314

0.196

Table IV

Relative Sensitivities (∂ρ/∂X)/(ρ/X) of Computed Albedo to the Sky Irradiance X = Es0 and X = Hs and Optical Depth Model Parameters X = τ0 and X = H for Horizontal Shadowed Targets at Various Altitudes for MSS Band 4; Other Parameter Values are Those of Fig. 14